Question

If m is a positive integer, which of the following could be true?

i. m² is a prime number.
ii. is a prime number.
iii. m² = square root m
a) i only
b) ii only
c) iii only
d) ii and iii

Answer 1

The statements that could be true are: ii) m is a prime number; and iii) m² = √m.

So option (D) is the correct answer

Step-by-step explanation:

To determine which of the given statements could be true, let's analyze each one:

If m² is a prime number, it implies that m must be either 1 or a prime number itself. For example, if m = 1, then m² = 1² = 1, which is a prime number. However, if m = 2, then m² = 2² = 4, which is not a prime number.

If m is a prime number, it implies that m² is also a prime number. For example, if m = 2, then m² = 2² = 4, which is a prime number.

If m² = √m, it implies that m = √√m. This equation only holds when m = 1.

Therefore, the statements that could be true are ii) m is a prime number and iii) m² = √m. So the correct answer is d) ii and iii.